In an article entitled “Algorithms for Ambiguity Function Processing,” published in the IEEE Transactions Acoustics, Speech, and Signal Processing, Vol. ASSP-29, No. 3, June 1981, Seymour Stein disclosed a method for calculating a complex ambiguity function (CAF) for narrow-band signals. Dr. Stein's method is not effective for processing wide-band signals.
In an article entitled “Joint Time-Scale and TDOA Estimation: Analysis and Fast Approximation,” published in the IEEE Transactions on Signal Processing, Vol. 53, No. 8, August 2005, Y. T. Chan and K. C. Ho disclosed an iterative method to maximize a CAF, which the authors renamed as a cross-ambiguity function, for wide-band and real-valued signals. Chan et al. employ time-scaling and time-difference-of-arrival (TDOA) in their method. Chan et al. improve upon Dr. Stein's method by disclosing a method that is capable of processing a wide-band signal. However, the method of Chan et al. exhibits precision problems at low signal-to-noise ratios (SNR) as the signal length becomes large. In addition, the method of Chan et al. does not process complex-valued signals.
There is a need for a method for processing wide-band signals of large length without losing precision and a method for processing wide-band complex valued signals. The present invention is such a method.
U.S. Pat. No. 5,500,648, entitled “GEOLOCATION RESPONSIVE RADIO TELECOMMUNICATION SYSTEM AND METHOD THEREFOR,” discloses a system where a subscriber unit communicates with a single satellite that uses a Doppler component, propagation duration, and real-time measurement signals to determine the geolocation of the subscriber unit. U.S. Pat. No. 5,500,648 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 5,526,001, entitled “PRECISE BEARINGS ONLY GEOLOCATION IN SYSTEMS WITH LARGE MEASUREMENTS BIAS ERRORS,” discloses a method that uses bearing rate of change to estimate emitter geolocation. U.S. Pat. No. 5,526,001 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Nos. 5,844,521 and 6,020,847, each entitled “GEOLOCATION METHOD AND APPARATUS FOR SATELLITE BASED TELECOMMUNICATIONS SYSTEM,” disclose devices for and methods of geolocating a mobile terminal by obtaining synchronization differential data to calculate least first and second geoposition lines. U.S. Pat. Nos. 5,844,521 and 6,020,847 are hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 6,285,319, entitled “METHOD FOR REDUCING GEOMETRICAL DILUTION OF PRECISION IN GEOLOCATION OF EMITTERS USING PHASE CIRCLES,” discloses a method of geolocating an emitter using at least one observer measuring signal change while moving on at least two observation tracks. U.S. Pat. No. 6,285,319 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Nos. 6,292,665 and 6,754,502, entitled “GEOLOCATION OF CELLULAR PHONE USING SUPERVISORY AUDIO TONE TRANSMITTED FROM SINGLE BASE STATION,” disclose methods of geolocation using angle of arrival and range information. U.S. Pat. Nos. 6,292,665 and 6,754,502 are hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 6,933,888, entitled “MULTI-SHIP COHERENT GEOLOCATION SYSTEM,” discloses a method of geolocating an emitter without requiring more than one platform to measure the same pulse from the emitter. U.S. Pat. No. 6,933,888 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 6,934,626, entitled “LOW-COST, LOW-POWER GEOLOCATION SYSTEM,” discloses a device for and method of geolocation by processing the magnitude of the transmitted signal. U.S. Pat. No. 6,934,626 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 7,132,961, entitled “PASSIVE RF, SINGLE FIGHTER AIRCRAFT MULTIFUNCTION APERTURE SENSOR, AIR TO AIR GEOLOCATION,” discloses a method of geolocation that uses batch-based recursive estimators. U.S. Pat. No. 7,132,961 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 7,187,326, entitled “SYSTEM AND METHOD FOR CUMULANT-BASED GEOLOCATION OF COOPERATIVE AND NON-COOPERATIVE RF TRANSMITTERS,” discloses a device for and method of geolocation that uses a transmitted signal's higher order statistics of temporally dependent waveforms. U.S. Pat. No. 7,187,326 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 7,268,728, entitled “MOVING TRANSMITTER CORRELATION INTERFEROMETER GEOLOCATION,” discloses a device for and method of geolocation that using direction-finding (DF) equipment. U.S. Pat. No. 7,268,728 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 7,286,085, entitled “PRECISION GEOLOCATION SYSTEM AND METHOD USING A LONG BASELINE INTERFEROMETER ANTENNA SYSTEM,” discloses a device for and method of geolocation that uses a long baseline interferometer antenna system. U.S. Pat. No. 7,286,085 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 7,315,280, entitled “COHERENT GEOLOCATION SYSTEM,” discloses a device for and method of geolocation that estimates the underlying repetition interval of the emitter. U.S. Pat. No. 7,315,280 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 7,391,355, entitled “SINGLE PLATFORM GEOLOCATION METHOD AND APPARATUS,” discloses a device for and method of geolocation that uses a single platform for determining a Doppler measurement set of a targeted aircraft or signal of interest. U.S. Pat. No. 7,391,355 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. No. 7,436,355, entitled “METHOD AND APPARATUS FOR GEOLOCATION DETERMINATION,” discloses a device for and method of geolocation that determines an approximate location of a receiver, a range difference between the receiver and the satellite, a median value of the range difference, and an offset value between the range difference and the median value. U.S. Pat. No. 7,436,355 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20050231425, entitled “WIRELESS WIDE AREA NETWORKED PRECISION GEOLOCATION,” discloses a device for and method of geolocation that uses a network of multitracking devices and a data link between the same to share information. U.S. Pat. Appl. No. 20050231425 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20060030332, entitled “METHOD AND SYSTEM FOR GEOLOCATION OF WIRELESS TRANSMISSIONS USING DISTRIBUTED PROCESSORS IN WIRELESS RECEIVER TOWERS AND A METHOD FOR COLLECTING A FEE FOR PROCESSING GEOLOCATION REQUESTS,” discloses a device for and method of geolocation that uses multiple cell towers. U.S. Pat. Appl. No. 20060030332 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 200701270.12, entitled “RATE-BASED RANGE AND GEOLOCATION,” discloses a device for and method of geolocation that determines the speed and direction of the platform, a line from the platform, an angle between the travel uses a network of multitracking devices and a data link between the platform and the line, a rate of change in the angle. U.S. Pat. Appl. No. 20070127012 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20070129085, entitled “SYSTEM AND METHOD OF OPERATION FOR NETWORK OVERLAY GEOLOCATION SYSTEM WITH REPEATERS,” discloses a device for and method of geolocation that determines if a signal is received directly or was passed through a repeater. U.S. Pat. Appl. No. 20070129085 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20070146203, entitled “METHOD AND APPARATUS FOR REDUCING GEOLOCATION AMBIGUITY IN SIGNAL TRACKING,” discloses a device for and method of geolocation that determines a first and second set of geolocations and comparing the sets to reduce ambiguity. U.S. Pat. Appl. No. 20070146203 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20070236389, entitled “REFERENCE BEACON METHODS AND APPARATUS FOR TDOA/FDOA GEOLOCATION,” discloses a device for and method of geolocation that estimates bias errors in TDOA and frequency-difference-of-arrival (FDOA). U.S. Pat. Appl. No. 20070236389 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20080151231, entitled “FIBER OPTIC TESTING SYSTEMS AND METHOD INCORPORATING GEOLOCATION INFORMATION,” discloses a device for and method of geolocation that gathers location data pertaining to a fiber optic network. U.S. Pat. Appl. No. 20080151231 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20080169978, entitled “DETECTION OF DECEPTION SIGNAL USED TO DECEIVE GEOLOCATION RECEIVER OF A SATELLITE NAVIGATION SYSTEM,” discloses a method of geolocation that detects the presence of a deception signal. U.S. Pat. Appl. No. 20080169978 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20080174490, entitled “STRUCTURED ARRAY GEOLOCATION,” discloses a device for and method of geolocation that computes a calibration factor for geolocations of multiple transmitters. U.S. Pat. Appl. No. 20080174490 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20080186235, entitled “MULTIPLATFORM TDOA CORRELATION INTERFEROMETER GEOLOCATION,” discloses a device for and method of geolocation where a plurality of samples are taken periodically, the samples are digitized, and Global Positioning System (GPS) stamps are added to the digitized samples. U.S. Pat. Appl. No. 20080186235 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20080252516, entitled “DETERMINING A GEOLOCATION SOLUTION OF AN EMITTER ON EARTH USING SATELLITE SIGNALS,” discloses a device for and method of geolocation that takes two TDOA measurements and an FDOA measurement. U.S. Pat. Appl. No. 20080252516 is hereby incorporated by reference into the specification of the present invention.
U.S. Pat. Appl. No. 20080252525, entitled “DETERMINING A GEOLOCATION SOLUTION OF AN EMITTER ON EARTH BASED ON WEIGHTED LEAST-SQUARES ESTIMATION,” discloses a device for and method of geolocation that uses least-squares estimation. U.S. Pat. Appl. No. 20080252525 is hereby incorporated by reference into the specification of the present invention.